Quote from uglyboy:
To try to answer your question Segv, if the distro is Cauchian rather than Gaussian, it implies that FOTM options are undervalued with respect to their probability of moneyness, and should be bought.
Perhaps you could play the spread between the prices predicted by the 2 distro models ...
The implication of the Cauchy assumption is that the mean is undefined, and therefore the variance and standard deviation are undefined. A random sample from a Cauchy distribution could easily
appear to be log-normal and leptokurtotic while the tails are out-of-sample. In a normal distribution we assume the probability of outliers approaches some infinitely small number, but if the distribution is Cauchy that assumption is flawed in the extreme. In other words, why is it that we do not simply sell OTM puts, buy OTM calls, and delta-hedge? Theoretical edge and positive expectancy are staring us all in the face, day after day, in the form of the skew. It is because if we change our assumptions and take the view that the underlying distribution is Cauchy, not only are FOTM options undervalued, but they are
grossly undervalued. These FOTM options are far better than any lottery ticket, they are the cheapest insurance policy on the planet.
To reiterate dagnyt's point, the take-away practical message here is nothing new, nothing you have not heard before. Its something that many option traders know intuitively without having some economist or mathematician explain probability distributions. It is simply to protect yourself from uncertainty in the form of owning extremely inexpensive insurance. And to uglyboy's point, yes there is absolutely a position that profits from the difference between these distributions, its called "short the atm long the wings"! Again nothing new or revolutionary.
But there
are some finer points embedded in this discussion that I think could be useful to some of you reading this thread. From a theoretical
and practical standpoint, what is the difference between selling a FOTM credit spread, or delta-hedging with a short ATM straddle? Ignoring the risk profiles for a moment, in the latter position one experiences first-hand the model that is built into the pricing of the former, but with arguably similar expectancy. We know empirically that higher anxiety is associated with trading activity in general, even among highly experienced traders[1]. Perhaps the desire to avoid this stress is part of the motivation of so agents in seeking a purely systematic approach, or in seeking a "theoretically perfect" spread.
Finally, I really got a chuckle out of the article uglyboy posted, where the gentleman from OptionVue went to the trouble of back-testing selling ATM combos and buying wings at 1 standard deviation over 5 years. He found that 65% of the positions were profitable. I mean, what were the chances of that happening, say about 68%?
[1] I do not have time to dig the references, try Scholar if you are interested, or PM and I might find them later.
--segv
